L(x,y) = +y-8x-8y- 2xy +203

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

A: To find the minimum distance from the given curve to the point using Lagrange multipliers method.…

Q: need help with 2and 3 not number 1 !!!

A: Let x and y be the length of sides of rectangle along x-axis and y-axis respectively. Then , the…

Q: A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base…

A: Given:

Q: Use the method of Lagrange multipliers to find the minimum distance from the origin (0, 0) to the…

A: We need to use the method of Lagrange's multiplier to determine the minimum distance from the point:…

Q: A company plans to manufacture a rectangular box with a square base, an open top, and a volume of…

A: The given box is in rectangular shape but has a square base with volume of the box as 452 cm3.So…

Q: Find two numbers such that their difference is 5 and their product is minimum.

A:

Q: 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the…

A: Product of two positive number is 750. The sum of one and 10 times of another is minimum.

Q: Suppose the labor cost (in dollars) for manufacturing a camera can be approximated by 3 L(x,y) = x²…

A: We will use partial derivative to find x and y.

Q: a. Find the radius and height of a cylindrical soda can with a volume of 256 cm that minimize the…

A: Part (a) Given data: The volume of can is V = 256 cm3.

Q: Suppose that f(x, y) = 4x* + 4y* – xy Then the minimum is

A:

Q: A rectangular box is to have a square base and a volume of 81 ft3. If the material for the base…

A:

Q: A worker is to construct an open rectangular box with a square base and a volume of 98 ft°. If…

A:

Q: A company is manufacturing a trash can with a volume of 4 cubic ft that has a cylindrical body and a…

A: The volume for a cylinder is πr2h and a hemisphere is 23πr3. As the trash can is of volume 4 cubic…

Q: What is the critical point of the total cost function TC = Q3-6Q2 – 640Q? 640Q ? %3D 1/3

A:

Q: find the point on the line y=2x+10 that is closest to the orgin, (0,0) What is the minimum distance?

A:

Q: A rectangular box is to have a square base and a volume of 16 ft3. If the material for the base…

A: Volume= x2y= 16 So, y= 16/x2   total cost:

Q: The productivity of a country is given by f(x,y) = 100x0.6°y0.37, where x is the amount of labor and…

A:

Q: what is the relative minimum value of the function f(x,y) = e^x^2 + y^2

A: Calculate first and second partial derivative with respect to x and y  then take first partial…

Q: A customer has made a request for a wooden box with an open top that needs to have a volume of…

A: Note:- As per your demand we solve it for only constraints for this optimization  Given problem:- A…

Q: Find the minimum distance from the parabola x – y = 0 to the point (0, 3). Minimum distance = %3!

A: At P(x,y), the point of shortest distance the slope of the line from P to (0,3) must be…

Q: Find the length L and width W (with W less than or equal to L) of the rectangle with area of 198…

A:

Q: The production function for a firm is p(x, y) = 72x"y"", where x and y are the number of units of…

A:

Q: Find the second iteration value of an extremum (maximum/minimum value) of f(x) = 5sin2x - bx2 - cx…

A: Given the function fx=5sin2x-2x2-4x. The initial guesses are x1=0, x2=1, x3=1.5. The Quadratic…

Q: Express y = 3x2 – 8x - 1 in the form y = 3(x – p)² + q, where p and q are constants and hence find…

A:

Q: a. If she walks at 3 mi/hr and rows at 2 mi/hr, at which point on the shore should she land to…

A: Given: A boat on the ocean is 4 mi from the nearest point on a straight shoreline; that point is 6…

Q: Suppose that a company needs 5 ×10,000 items during a year and that preparation costs are $5 for…

A:

Q: Find the point where the function f(x,y, z) = x + 2y + 3z subject to the I takes on its minimum…

A: The given function is f(x,y,z)=x+2y+3z.

Q: Find the minimum value ofx +y +z² given x+y+z=3a.

A:

Q: Suppose that f(1, y) = 2z² + 2y – zy Then the minimum is

A: Given: fx,y=2x4+2y4-xy We need to find the minimum value of the given function.

Q: Suppose the labor cost (in dollars) for manufacturing a camera can be approximated by L(x,y) = x² +…

A: Given: The labor cost(in dollars) for manufacturing a camera is approximated by, L(x,…

Q: Suppose that the total cost (in dollars) of producing a product is C(x, y) = 15 + 3x2 + 5y2, where…

A: C(x, y) = 15 + 3x2 + 5y2, x is the cost per pound for material and  y is the cost per hour for…

Q: A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base…

A:

Q: By minimizing the function ƒ(x, y, u, y) = (x - u)2 + (y - y)2 subject to the constraints y = x + 1…

A:

Q: 18. If the total cost function for a product is C(x) = 300 + 10x + 0.03x² dollars, producing how…

A: Question number 18,Given,            The total cost function for a product is Cx=300+10x+0.03x2…

Q: Express y = 3x2 – 8x - 1 in the form y = 3(x – p)² + q, where p and q are constants and hence find…

A: To express in the form y=3(x-p)²+q

Q: What is the maximum vertical distance between the y=x+2 and the parabola y=x^2 for -1 is less than…

A:

Q: Find the minimum distance from the point (2, 1, 9) to the surface x + y + z = 9.

A:

Q: Find the maximum and minimum attained by f(x, y) = 3xy + 2x + 3y in x2 + y < 1. You must use…

A:

Q: A satellite television reception station is to be located at point P so that the sum of the squares…

A:

Q: Assume that it costs Apple approximately C(x) = 25,600 + 100x + 0.01x² dollars to manufacture x 32GB…

A: We use second derivative test to find out minimum average cost

Q: Suppose the labor cost (in dollars) for manufacturing a camera can be approximated by L(x,y)=…

A: Given :Lx,y=32x2+y2-3x-6y-2xy+101

Q: what is the relative minimum value of the function f(x,y)= xy + 4/x + 2/y

A:

Q: Find the maximum and minimum volumes of a rectangular box whose surface area equals 8000 square cm…

A: Let the three sides or edges of the rectangular box be a,b and c in cm. Surface area of the box will…

Q: Find the point where the function f(x,y,z) = x + 2y + 3z subject to the constraint xyz= 2 takes on…

A: Answer is in below steps.

Q: The amount of space required by a particular firm is f(x, y) = 1000(6x2 + y2)^1/2, where x and y…

A:

Q: A cable runs along the wall from C to P at a cost of $3 per meter, and straight from P to M at a…

A: AC = 18, AM= 8 (given)  CP = x , AP = AC-PC = 18-x  In △APM , PM2 = AP2 +AM2…

Q: Suppose the labor cost (in dollars) for manufacturing a camera can be approximated by L(x.y) =x +y -…

A: Given: Suppose the labor cost in dollars for manufacturing a camera can be approximated by Lx,…

Q: A storage box with a square base must have a volume of 90 cubic centimeters. The top and bottom cost…

A: